After doing some math it actually seems a little low
3 times a week comes out to about 10.3 years
4 times a week comes out to about 7.7 years
6 times a week comes out to about 5.12 years
They typically say it takes ~10 years but most BBs I know have been pretty damn dedicated and hit training a lot more then 3 times a week

Well, to be fair, it does say 'minimum amount of time'. The reason I ask is twofold:

1) The Aikido that myself, my wife, and sister-in-law go to records your actual hours in class, and so does the BJJ class I just signed up for today (but haven't attended yet).

2) I'm new to this whole bit, and am still more than a little in the dark about how it all works. Generally speaking, it (until I thought about this) seemed to me that promotion would be based (in a perfect world) strictly on merit and ability, does the Time in Service really matter so much? If it does, would someone be so kind as to explain why? (I'm not doubting the validity of an argument for TIS, I just don't understand it).

I think the instructor needs/wants to see not only how you perform (in training or competition), but also your attitude towards the sport and the team, which is - together with your technical progress - best seen when you train regularly.

CLICK & WATCH: I got BULLSHIDO ON TV!!!
"Bruce Lee sucks because I slammed my nuts with nunchucks trying to do that stupid **** back in the day. I still managed to have two kids. I forgive you Bruce." - by Vorpal

I don't think their is someone sitting around with one of those clicky things that click the button every time you show up.
As I said a bit earlier it seems about right if not a little short of what the actual number tends to be.
The nice thing about a martial art like BJJ or Judo is you have a pretty good approximation to what skill level you are at. It is actually rather hard on the ego for some time cause you know exactly how much you suck.
However with time you will notice that you can really do this thing and that the time on the mat makes the difference as new people come into the gym.

I do know some schools are quite rigorous about record keeping, sign in cards for each student etc.
Others apparently don't really care to do so and play it more by ear, so it varies quite a bit it seems.
Other than that, agreed.

Excellent input, guys :D
I definitely appreciate it. I just watched Ed O'neill get his black belt in a youtube vid, that was awesome.
Out of curiosity - I heard that quite a few choke at blue belt, and don't get any farther - is there a reason for that? (I also heard that blue belt is one of the longest TIS belts - again, is this true? If it is, or was for you, would you tell me why, in your opinion?)
Thanks, y'all.